Co integration beteweem historical volatilities series

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cedbourge
Posts: 6
Joined: Fri Oct 05, 2012 11:54 am

Co integration beteweem historical volatilities series

Postby cedbourge » Thu Jun 13, 2013 9:55 am

Hi Carole,

I am looking at verifiying if 2 volatilities time series are co-integrated or not (how one vega can be hedged with another one in the long run ?).

The 2 volatilies time series I have are based on historical stdev (so the volatilities times series are coming from a rolling windows historical stdev).

My 2 vols series are stationary I(0) so there is no point in using co integration to check for long term strenght of the relatiionship...at the same time the correlation between the 2 vol series is relatively high (80%) but the spread between the 2 vol series diverge.

So I would like to use something more powerful than just the correlation...that should be the co integration...but it doesn't apply as the series are stationary....is there something else I could use to capture long term movement between vols ?

Many thanks
Cedric.

coalexander
Posts: 815
Joined: Sun Sep 28, 2008 10:30 pm

Re: Co integration beteweem historical volatilities series

Postby coalexander » Thu Jun 13, 2013 5:51 pm

Hi,

Long term co-movements can be determined by the behaviour of the spread even if the series are statistically I(0)...but in your case you have a problem because you say the spread is not I(0). The problem is that you do not account for jumps.

Volatilities jump a lot, so you need to use the new generation of unit tests and cointegration tests, which is robust to jumps. This is really advanced econometrics...if you are able to understand this sort of thing, then this chap may be able to point you in the right direction: http://ideas.repec.org/e/pcz10.html

Cheers, Carol

cedbourge
Posts: 6
Joined: Fri Oct 05, 2012 11:54 am

Re: Co integration beteweem historical volatilities series

Postby cedbourge » Fri Jun 14, 2013 10:31 am

Hi Carole,

I will definetly will look at the paper you mentionnned (is this the fractional cointegration test ?)

Generllay banks have a lot of derivative (options) based on unobservable vol...to mark their illiquid vol trader use a histo spread to a more liquid vol and they will hedge the illiquid vega with the more liquid one. Then we have to estimate some PnL reserve which will be generally based on the netted risk between the illiquid vega and the liquid vega. The more we assume netting between vegas the less the reserve. Moreover, the degree of netting will depend on the strenght of the relationship between the 2 vols.

So far we only look at the correlation between the volatilities to assess the strenght of relationship. For example we conclude that if correl is 70% then 70% of the vegas can be netted...this an awful rule of thumb as correlation is too much time dependent, difficult to measure ect...

So I am trying to introduce the concept of co integration to some senior traders and quant in order to setup a more meaningful netting rule. For example it would be good to come up with a rule such as if the 2 series are not co integrated then no netting will be allowed (even if the correl seems quite high).

In my particular example I though this was a good example : the vols correl is quite high (80%) but the vols spread diverge. Hence I would have like to prove that the series was not co integrated and hence no netting should be allowed...but I can't do this as the 2 vols series are I(0)...

When you say that "long term co movement can be determined by the behaviou of the spread"...are you suggesting to test for the spread unit root ?

Also I am wondering to which extend we need to perform deeper co integration test : only looking at the graph seems obvious to see that the 2 vols level diverge..so why bother doing co integration test or unit root test on the spread or other more complex stat test ? ( I would like to make the audience aware of the need to go further than just graph view...but I don't know how ?).

If say after accounting for jumps I find the spread to finally be I(0) what conclusion shall I draw in term of static hedge efficiencies (and hence degree of netting).


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